The assassination of Ahmed al-Jabari in a missile strike in Gaza City was the "start of a broader operation", the Israel Defence Forces has confirmed.

Ground forces are on stand-by to enter Gaza if given the order, it said via Twitter, and gunships continue firing shells into the coastal strip.

In response, Hamas's armed wing warned al-Jabari's assassination "had opened the gates of hell" and vowed its militants would "continue the path of resistance”.

Israel hit more than 20 “targets” inside Gaza after it assassinated the Islamist military leader, along with another Hamas official, in a missile strike against the car in which they were travelling.

The Israeli prime minister, Binyamin Netanyahu, warned that the military was "prepared to expand" its Gaza operation.

The IDF said its actions were part of a wider Israeli operation against militant groups and weapon sites in the Hamas-run Gaza Strip, and were prompted by a wave of rocket attacks against Israel.

Gaza’s health ministry says 10 civilians have been killed, including two young children – an 11-month-old and a six-year-old – while at least 45 people have been wounded, 10 of them in critical condition.

There were scenes of chaos at Shifa Hospital in Gaza City, as dozens of seriously injured patients were stretchered in, while ambulances sped off to collect more casualties.

Meanwhile, in southern Israel, residents have been ordered to stay in bomb shelters in preparation for an expected surge in rocket attacks from Gaza. Schools in a 40km radius of the border have closed.

Hamas, an Islamist movement considered a terrorist group by Israel, the U.S. and European Union, has appealed for help from the new Muslim Brotherhood leaders of Egypt.

Egypt's new President Mohamed Mursi recalled of the country’s ambassador to Israel and called for an urgent meeting of the Arab League. The Egyptian foreign minister, Mohamed Kamel Amr, called on Israel to stop the strikes immediately, warning any further escalation from Israel "could have negative repercussions on the security and stability of the region".

Thirteen rockets fired from Gaza into southern Israel had been intercepted by the country’s missile defence system, the IDF spokesperson said, tweeting with the tag #PillarofDefense.

“We recommend that no Hamas operatives, whether low-level or senior leaders, show their faces above ground in the days ahead," the spokesperson said.

Saeb Erekat, a member of the Palestine Liberation Organisation executive committee and chief Palestinian negotiator condemned the attacks as an attempt to "initiate a bloody escalation".

"We hold the Israeli government fully responsible for the consequences that this new act of aggression would bring to the region." he said. “This exposes that Israel has an agenda for war but not for peace.”

In a press conference held overnight, Israel's defence minister Ehud Barak said Israel was not interested in engaging in war, but that Hamas’s provocation over the past few days had forced it to act.

One Gaza resident, a doctor, posted this on her Facebook page as the Israeli bombardment continued: “Gaza is under extensive Israeli military attack … the hospitals are already lacking essential emergency medications, and citizens were called for blood donation, we do not have power … we expect more escalation.”

The video of al-Jabari’s assassination was posted on YouTube by the Israeli Defence Force. Just 14 seconds long, it is shot from the air, following a car along an urban street before a missile strike all but obliterates the sedan.

Al-Jabari is the most senior Hamas operative to be killed by Israel in almost four years, since Operation Cast Lead, its three-week assault on Gaza, left about 1400 Palestinians dead.

He was widely believed to have been intimately involved in the Hamas takeover of Gaza in 2007, and played a key role in overseeing the imprisonment of Israeli soldier Gilad Shalit, who was snatched by Palestinian militants while on a patrol near the Gaza Strip in 2006 and held in secret locations in Gaza until his release in October 2011, in return for the release of 1027 Palestinian prisoners.

In a rare public appearance, al-Jabari personally escorted Shalit to the Rafah Crossing with Egypt as part of the prisoner exchange.

Israel's air strikes have prompted anger, fear and panic in Gaza, with residents anticipating a prolonged Israeli military campaign. Some are at shops stocking up on bread and essentials, while others are crowding outside the coastal strip’s hospital and morgues in a vigil for the injured and to mourn the dead.

The Muslim Brotherhood’s Freedom and Justice Party issued its own condemnation. "Israel's return to the policy of assignation of leaders from the Palestinian struggle groups shows that the Israeli occupation wants to drag the region towards instability.”

In Australia, the Department of Foreign Affairs and Trade reviewed and reissued its travel advisory for Israel and the Gaza Strip. The travel advisory has not been upgraded, however it contains new information about the attacks overnight.

Australians have been urged to exercise a high degree of caution in Israel overall, while travellers have been warned to reconsider their need to travel in Bethlehem, Ramallah and Jericho, and have been advised not to travel in the Gaza Strip, including surrounding areas, and the remainder of the West Bank.

‘‘We strongly advise you not to travel to areas around the Gaza Strip in southern Israel due to the possibility of mortar and rocket fire,’’ the advisory says.

‘‘A significant escalation occurred in October 2012. A further escalation may occur following the commencement of Israeli military operations against the Gaza Strip on 14 November 2012. A number of Israeli cities in the south, including Ashdod (30kms to the north of the Gaza Strip) and Be’er Sheva (40kms to the east of the Gaza Strip) have previously been struck by rockets fired from the Gaza Strip.’’

Australians or their families in need of emergency assistance have been urged to call the 24-hour consular emergency centre on 1300 555 135 within Australia, or +61 2 6261 3305 from outside Australia.

DFAT said it was not immediately clear whether any Australians had been caught up in the violence.